If the light is AC, you can just use a standard wall outlet and plug it in. If you want to use a solar light on a 120 volt outlet, you will need to buy an inverter.
In order to connect the light to two different voltages, you need a deep battery rated at 150 amps. This is to ensure there is enough electricity to power the lights on cloudy days. Also, the higher the battery capacity, the larger the solar array must be. If the light is too large, try connecting an incandescent light. LED lights charge faster because they have a wider range than incandescent bulbs.
To test the voltage of the socket, you can use a multimeter. 120-volt outlets are common in North American homes. The bidirectional voltage difference should be within 230 volts. If the voltage is higher than 120 volts, you should seek the help of a licensed electrician. Alternatively, you can use a voltmeter to test the voltage at the electrical outlet.
You should also know that LED lights and strips use very little power. They don't use a lot of electricity and don't increase your electricity bill over time. They also won't cause your house to overheat. Because 95% of electricity is used to generate light, LED lights won't make your home too hot. So you'll save on electricity bills and don't have to worry about overheating your LED lights.
